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3 years ago

How do i solve this as an inequality?a. 2x+6 <14please send a step by step!! :)

Mathematics

2 answers:

Y_Kistochka [10]3 years ago

6 0

Answer:

2x+6<14

2x<14-6

2x<8

x<4

Leokris [45]3 years ago

4 0

Answer: x<4

Step-by-step explanation:

2x+6<14

2x+6 -6<14 - 6

2x < 8

2x(/2) < 8(/2)

X<4

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9. A circle has an arc of length 56pi that is intercepted by a central angle of 120 degrees. What is the radius of the circle?

SSSSS [86.1K]

Answer:

Part 4) $r=84\ units$

Part 9) $sin(\theta)=-\frac{\sqrt{5}}{3}$

Part 10) $sin(\theta)=-\frac{9\sqrt{202}}{202}$

Step-by-step explanation:

Part 4) A circle has an arc of length 56pi that is intercepted by a central angle of 120 degrees. What is the radius of the circle?

we know that

The circumference of a circle subtends a central angle of 360 degrees

The circumference is equal to

$C=2\pi r$

using proportion

$\frac{2\pi r}{360^o}=\frac{56\pi}{120^o}$

simplify

$\frac{r}{180^o}=\frac{56}{120^o}$

solve for r

$r=\frac{56}{120^o}(180^o)$

$r=84\ units$

Part 9) Given cos(∅)=-2/3 and ∅ lies in Quadrant III. Find the exact value of sin(∅) in simplified form

Remember the trigonometric identity

$cos^2(\theta)+sin^2(\theta)=1$

we have

$cos(\theta)=-\frac{2}{3}$

substitute the given value

$(-\frac{2}{3})^2+sin^2(\theta)=1$

$\frac{4}{9}+sin^2(\theta)=1$

$sin^2(\theta)=1-\frac{4}{9}$

$sin^2(\theta)=\frac{5}{9}$

square root both sides

$sin(\theta)=\pm\frac{\sqrt{5}}{3}$

we know that

If ∅ lies in Quadrant III

then

The value of sin(∅) is negative

$sin(\theta)=-\frac{\sqrt{5}}{3}$

Part 10) The terminal side of ∅ passes through the point (11,-9). What is the exact value of sin(∅) in simplified form?

see the attached figure to better understand the problem

In the right triangle ABC of the figure

$sin(\theta)=\frac{BC}{AC}$

Find the length side AC applying the Pythagorean Theorem

$AC^2=AB^2+BC^2$

substitute the given values

$AC^2=11^2+9^2$

$AC^2=202$

$AC=\sqrt{202}\ units$

$sin(\theta)=\frac{9}{\sqrt{202}}$

simplify

$sin(\theta)=\frac{9\sqrt{202}}{202}$

Remember that

The point (11,-9) lies in Quadrant IV

then

The value of sin(∅) is negative

therefore

$sin(\theta)=-\frac{9\sqrt{202}}{202}$

5 0

3 years ago

X = 22 + 10x<br> How to find x?

GrogVix [38]

Answer:

x = -2.44

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract 10x from both sides:

x (-10x) = 22 + 10x (-10x)

x - 10x = 22

-9x = 22

Isolate the variable, x. Divide -9 from both sides:

(-9x)/-9 = (22)/-9

x = 22/-9

x = -(22/9)

x = -2.44 (repeating).

x = -2.44 (rounded) is your answer.

7 0

3 years ago

The end of the cave is 380 meters below surface of the earth generate an integer to reoresent this profit

RSB [31]

The question says that the end of the cave is 380 meters below.

Lets say the sea level or the surface is at 0 meters or we can say that it is the reference level for us.

Now if we go up the height will be measured with positive integer but if we go down the depth will be represented by a negative integer.

Negative integer also represents the depth or the distance below the surface level.

Here we need to generate an integer that can represent the depth of 380 meters.

So if we are going down we will use negative integer to represent.

Therefore, the integer to represent the depth is $-380$ meters.

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3 years ago

2. Hanna is making some delicious Tollhouse chocolate chip cookies. She wants to

loris [4]

Answer:

ano yung sasagotan Gan?

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2 years ago

Erika had three pieces of ribbon . Each piece is 25 yards long. She needs to cut pieces that are 22 inches long . What is the gr

Kisachek [45]

B. 120 because you cant glue the ribbon together, simply multiply 25 by 3 multiply that by 12 divide that by 22 then multiply that by 3

4 0

3 years ago

How do i solve this as an inequality?a. 2x+6 <14please send a step by step!! :)​

How do i solve this as an inequality?a. 2x+6 <14please send a step by step!! :)